以零位渦外流理論探討浮力驅動沿岸流結構

Abstract

本研究以三維的海洋數值模式(Regional Ocean Modeling System, ROMS)探討Thomas and Linden (2007 ; 以下簡稱為TL07)所提出的浮力驅動沿岸流結構理論，理論中考慮兩層流體近似下，一層低密度的均勻流體於另一層高密度的均勻流體上，沿著海岸往開爾文波方向傳遞，並假設沿岸流中任何地方都要滿足零位渦度且地轉平衡。TL07表示，基於這些假設下，只要給定二流體的密度差(即減重力)與流量，即可以決定沿岸流的厚度、寬度以及厚度平均流速。 本研究的結果顯示，ROMS模擬的浮力驅動沿岸流滿足了TL07理論中所提及的地轉平衡假設，代表非絕熱(如流體介面上的剪應力(interfacial stress))，與平流效應在沿岸流的跨岸方向動量平衡中，為次要的物理過程，另一方面，沿著流線上的位渦度值也接近守恆。在一系列的流量實驗中，研究結果顯示模式模擬的沿岸流厚度與理論預測的結果有良好的一致性，然而，在沿岸流寬度上的預測結果則顯現出較明顯的差異，大致上預測結果有10～20％的低估情形，在靠近河口源頭的小部分地區有超過50%的低估情形，上述的研究結果顯示TL07理論在模式模擬的海洋環境下依然有合理的預測結果。然而，本研究發現模式結果並不滿足TL07理論中的零位渦度假設，此外，沿岸流中的鹽度場有著連續的變化，也意謂著兩層流體近似的前提在模式中並不適合。進一步的分析發現，因零位渦度與兩層流體近似假設而產生的兩誤差大致上互相抵消，因此，TL07理論對沿岸流結構的預測性並非基於正確的物理假設，而是兩誤差相互抵銷的結果。

A theory for the structure of buoyancy-driven coastal currents by Thomas and Linden (2007; TL07 hereafter) is tested using a three-dimensional, primitive equation ocean model (ROMS). The theory is under a two-layer approximation, considering a uniform layer of low-density water over high-density ambient. Under the influences of buoyancy forcing and Earth’s rotation, the resulting low-density water moves along a coastal wall in the direction of Kelvin wave propagation, forming a coastal current. In addition to the two-layer approximation, TL07 further assumed that the coastal current is geostrophically balanced and is characterized by zero potential vorticity (PV) along its path. Under the above assumptions and given the density contrast and flow rate, TL07 then predicts the coastal current thickness, width, and layer-averaged velocity. ROMS simulations show that the coastal currents indeed satisfy the geostrophic balance in cross-shore direction, and their PV is approximately conserved following the streamlines. For a range of flow rates, the thickness of simulated currents is in good agreement with the theory. The width shows some discrepancies. The theory underestimates the width by, on average, 20 percent, but underestimation increases to more than 50 percent near the riverine source. In general, though, TL07 has a reasonable predictive skill for the coastal current thickness and width. However, further examining TL07’s assumptions reveal that zero PV is not supported by the numerical model results. In addition, the density field varies continuously within the simulated coastal currents, rendering the layer-averaging approach questionable. It is demonstrated from theoretical derivations that the errors due to these two questionable assumptions largely cancel each other. Therefore, the observed predictive skill of TL07 may not have a sound physical basis.